I don't agree with you, movies.
The natural of xylitol, the carbon 3 is attached by two stereogenic groups (also H & OH), one is (R)configuration while another one is (S) form, you can figure them out.
(R) and (S) are assigned to two different groups, so, the carbon 3 is attached to 4 different groups and it is a stereocenter. However, it is achiral due to the plane of symmetry.
By changing one of the stereogenic groups, e.g. (S) -> (R), now, the carbon 3 is attached by 2 identical groups, 2 (R) groups. Therefore, it is not a stereocenter anymore, but it is chiral, no plane of symmetry.